A nonintrusive hybrid neural-physics modeling of incomplete dynamical systems: Lorenz equations

This work presents a hybrid modeling approach to data-driven learning and representation of unknown physical processes closure parameterizations. These models are suitable for situations where the mechanistic description dynamics some variables is unknown, but reasonably accurate observational data can be obtained evolution state system. In this work, we propose machine account missing physics then assimilation correct prediction. particular, devise an effective methodology based on recurrent neural network model dynamics. A long short-term memory (LSTM) correction term added predictive in order take into hidden physics. Since LSTM introduces black-box part model, investigate whether proposed neural-physical further corrected through sequential step. We apply framework weakly nonlinear Lorenz that displays quasiperiodic oscillations, highly chaotic two-scale model. The neural-physics yields results with predicted close true trajectory. For deviates from due accumulation prediction error one time step next ensemble Kalman filter takes updates diverged using available observations provide more estimate successful synergistic integration low-dimensional system shows potential benefits hybrid-neural complex dynamical systems.